ts angles measure 1100 and the radius of its sphere is 1 km

ts angles measure 1100 and the radius of its sphere is 1 km. Find the area of a \'kite\' shaped quadrilateral on a sphere of radius 10 mi if its four angles are /2, 56, |2,and /3. A1.9 A110 Find the measure of the angles of an equilateral triangle on a sphere if the area on the triangle is a fourth of the area of the sphere.

Solution

1) area of quadrilateral on a sphere is given by

A = r^2 ( sum of all angles - 2pi )

A = r^2 ( pi/2 + 5pi/6 + pi/2 + pi/3 - 2pi )

A = 100 ( pi/6 )

Area = 52.33 square miles